Via solution transformations

Lepidocrocite transforms to goethite in acid sulphate solution (Krause et al., 

1934 Nitschmann, 1938 van Oosterhout, 1967 Bechine et al., 1982). The process involves a dissolution-reprecipitation mechanism and is promoted by the presence of Fe ions which assist dissolution of lepidocrocite (see Chap. 12) the level of Fe may be increased by addition of metallic iron to the system. 

At temperatures of up to 70 °C, akaganeite grown by hydrolysis of FeCl3 is stable for months in the acidic mother liquor (Cornell, 1992). If, however, the system is seeded with goethite or hematite, the akaganeite gradually transforms into these com- 

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Although this type of transformation can take place in solution, usually under hydrothermal conditions, it has been most intensively investigated in the dry state. A precise separation of a transformation in the dry state from that in the presence of vater is, ho vever, often difficult because the minimum amount of water with which a via-solution transformation is still possible may be very small (see 14.3.5). This applies especially to poorly ordered and nano-sized oxides, such as ferrihydrite, with high surface areas and, therefore, high amounts of adsorbed water. 

In this case, d (nm) is the diameter of spherical particles. Both sets of equations are only approximations, particularly for goethite, the particles of which are often acicular. However, they do enable an estimate of the rise in solubility, as particle size drops, to be obtained (see Fig. 8.3). There is little difference between the results calculated using the two sets of equations for particles >100 nm, but for 10 nm particles there is more than an order of magnitude difference between the two equations. The higher solubility of smaller particles may lead to their transformation to larger ones via solution, a process called Ostwald ripening. 

Thermal transformation of solid phases in the dry state or via solution (Chap. 14)... 

The oxidation and hydrolysis of Fe leads to Fe " oxides either directly or via soluble green rust complexes, solid green rusts or Fe(OH)2. The latter convert to the oxides either by a solid state reaction or a via solution (reconstructive) transformation. Generally, where there is a difference between the structure of the precursor and that of the final oxide, a via solution process seems more likely, but internal rearrangement during topochemical oxidation to the new phase, may also take place. 

Schwertmannite is metastable with respect to goethite, except at very low pH (ca. < 3) and in the presence of potassium when jarosite is stable. Schwertmannite, therefore, transforms spontaneously to goethite via solution at 25 °C... 

Under hydrothermal conditions (150-180 °C) maghemite transforms to hematite via solution probably by a dissolution/reprecipitation mechanism (Swaddle Olt-mann, 1980 Blesa Matijevic, 1989). In water, the small, cubic crystals of maghemite were replaced by much larger hematite rhombohedra (up to 0.3 Lim across). Large hematite plates up to 5 Lim across were produced in KOH. The reaction conditions influenced both the extent of nucleation and crystal morphology. The transformation curve was sigmoidal and the kinetic data in water and in KOH fitted a first order, random nucleation model (Avrami-Erofejev), i.e. 

As lepidocrocite is metastable relative to goethite, it can be expected that lepidocrocite may transform into goethite. As demonstrated in the laboratory, this transformation proceeds via solution (see Chap. 14). Electron micrographs from a redoxi-morphic soil in Australia indicate that the same process seems to occur in soils (Fig. 16.5). The lepidocrocite crystals show dissolution features and there are small, acicu-lar, goethite crystals in their neighbourhood. Feroxyhyte was reported in two allopha-... 

In computational practice, such solutions are restricted by the approximation that the solvent is uniform and isotropic. It defines in the real space the susceptibility kernel as x(r, r ) = x( (r - f ). The counterpart in the -domain obtained via Fourier transform, reads x(k) = x(k), where k = k. The representation for s is similar. Parameterization... 

Various decomposition reactions of heterocyclic cations in aqueous solution are expected to proceed via pseudobase intermediates. These intermediates have been established for the alkaline decomposition of the pyridinium ring of nicotinamide adenine dinucleotide300 and for various solution transformations of flavin-derived cations.112,113,301-303 Nucleophilic substitution by hydroxide ion in various heteroaromatic cations almost certainly proceeds via the appropriate pseudobase tr-complexes.304,305... 

One solution to the problem of limited accuracy is to evaluate the kinetic energy matrix elements not in position but in momentum space connected via Fourier transformation [10,45]. In momentum space, the kinetic energy operator is diagonal and the associated matrix elements can be calculated by simple multiplication, followed by a back transformation to position space. 

Gondim, R.R., Cotta, R.M., Santos, C.A.C., and Mat, M. (2003) Internal Transient Forced Convection with Axial Diffusion Comparison of Solutions Via Integral Transforms, ICHMT International Symposium on Transient Convective Heat And Mass Transfer in Single and Two-Phase Flows, Cesme, Tmkey, August 17 - 22. 

Forced hydrolysis of Fe solutions involves hydrolysing Fe(N03)3, Fe(C104)3 or FeCls solutions at a temperature close to 100 °C under strongly acidic conditions (pH 1-2). It is believed that, if hematite is prepared from Fe(N03)3 or Fe(C104)3, it forms from Fe hydroxy species (Johnston and Lewis, 1983, 1986), whereas, if hematite is prepared from FeCls, akaganeite may be an intermediate product which then transforms to hematite via solution (Hamada and Matijevic, 1981). 

A theoretical estimate of the temperature course at the inner wall surfaces of a 200 1 extraction vessel (solution via Laplace transformation) is shown in Figure 10. The recognisable deviations from the experimentally-measured course are attributed both to the decrease in heat transfer with time and to the lack of consideration of the enthalpy of solidification which is released during the formation of dry ice. It has also proved necessary to record the local temperatures which differ greatly during pressure release. 

This equation is amenable to solution via Laplace transforms, so transforming with... 

Iron oxides are the most abundant metallic oxides in soils (Schwertmann and Taylor, 1989 Cornell and Schwertmann, 1996 Bigham etal., 2002). Iron oxides usually form via solution from Fe + ions released from Fe(II)-bearing silicates and sulfide minerals on weathering (Oades, 1963 Schwertmann and Taylor, 1989 Cornell and Schwertmann, 1996). Once formed in soil and other natural environments, the mineral phase, composition, and distribution of iron oxides can be continually modified by the alteration of their environments (Schwertmann and Taylor, 1989). Therefore, the formation and transformation of pedogenic iron oxide mineral phases depend on the pedo-environmental conditions under which they have formed. 

In most work on zeolite synthesis, crystallization is assumed to occur via solution-mediated transformations. In some cases the participation of the solid amorphous phase in the formation of nuclei has been clearly established [160]. 

As explained by Cook and Zhu (2005), the non-linear model yields infinite number of solutions. This is due to the fact that if (u, v ) is optimal, then (au, av ) is also optimal for a > 0. The non-linear formula can be converted to the equivalent linear programming problem via the transformation developed by Charnes and Cooper (1962) for linear... 

Stephens, J. S., S. R. Fahnestock, R. S. Farmer, K. L. Kiick, D. B. Chase, and J. F. Rabolt (2005). Effects of electrospinning and solution casting protocols on the secondary structure of a genetically engineered dragline spider silk analogue investigated via Fourier transform Raman spectroscopy. Biomacromolecules 6(3) 1405-1413. 

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